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Geomechanicsofsubsidenceabovesingleandmulti-seamcoalmining
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DOI:10.1016/j.jrmge.2015.11.007
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Accepted Manuscript
Geomechanics of subsidence above single and multi-seam coal mining
A.M. Suchowerska Iwanec, J.P. Carter, J.P. Hambleton
PII: S1674-7755(16)00015-9
DOI: 10.1016/j.jrmge.2015.11.007
Reference: JRMGE 228
To appear in: Journal of Rock Mechanics and Geotechnical Engineering
Received Date: 8 June 2015
Revised Date: 2 November 2015
Accepted Date: 16 November 2015
Please cite this article as: Iwanec AMS, Carter JP, Hambleton JP, Geomechanics of subsidence abovesingle and multi-seam coal mining, Journal of Rock Mechanics and Geotechnical Engineering (2016),doi: 10.1016/j.jrmge.2015.11.007.
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Geomechanics of subsidence above single and multi-seam coal mining
A.M. Suchowerska Iwanec1, J.P. Carter2*, J.P. Hambleton2
1 Golder Associates, Sydney, Australia.
2 ARC Centre of Excellence for Geotechnical Science and Engineering, The University of Newcastle, Newcastle, Australia
Received 8 June 2015; received in revised form 2 November 2015; accepted 16 November 2015
Abstract: Accurate prediction of surface subsidence due to the extraction of underground coal seams is a significant challenge in geotechnical engineering. This task is further
compounded by the growing trend for coal to be extracted from seams either above or below previously extracted coal seams, a practice known as multi-seam mining. In order to
accurately predict the subsidence above single and multi-seam longwall panels using numerical methods, constitutive laws need to appropriately represent the mechanical
behaviour of coal measure strata. The choice of the most appropriate model is not always straightforward. This paper compares predictions of surface subsidence obtained using
the finite element method, considering a range of well-known constitutive models. The results show that more sophisticated and numerically taxing constitutive laws do not
necessarily lead to more accurate predictions of subsidence when compared to field measurements. The advantages and limitations of using each particular constitutive law are
discussed. A comparison of the numerical predictions and field measurements of surface subsidence is also provided.
Key words: mining; coal; longwall mining; subsidence; multi-seam mining; constitutive modelling
1. Introduction
Empirical methods are mainly used in Australia and elsewhere for
predicting ground subsidence induced by mining. However, the primary
limitation of empirical prediction methods is that generally they cannot be
used with great confidence when predicting subsidence in new mining
environments, at least until the methods have been calibrated locally. A large
database of recorded field measurements of subsidence applicable to those
new environments is usually required for such calibrations. In this context,
new mining environments include mining in different geological conditions or
the use of a new mining method or approach, e.g. multi-seam mining.
Numerical modelling, when used as an alternative or indeed an adjunct to
empirical techniques, can predict subsidence in any environment, at least in
principle, if a sound knowledge of the geology, particularly the stratigraphy,
and the material behaviour of the subsurface strata are available. However,
currently, the prediction of subsidence using numerical modelling is renowned
for poor accuracy (Coulthard and Dutton, 1988; Kay et al., 1991; Mohammad
et al., 1998; Esterhuizen et al., 2010), and this stems in large part from a lack
of understanding of the constitutive laws of the coal measure strata.
There have been several subsidence studies conducted previously for a
range of constitutive laws describing the material behaviour of coal measure
strata (e.g. Kay et al., 1991; Lloyd et al., 1997; Coulthard and Holt, 2008), but
there has been no single study conducted to date that provides a
comprehensive assessment of the effectiveness with which commonly used
constitutive laws can predict surface subsidence and subsurface displacements.
The present study compares predictions obtained by modelling the coal
measure strata with constitutive laws of varying complexity in the
displacement finite element method (DFEM). Two different mining scenarios
are considered, i.e. a single seam super-critical longwall panel and multi-seam
mining involving first the extraction of super-critical longwall panels and then
*Corresponding author. Tel: +61 438602300;
E-mail address: [email protected]
the extraction of longwall panels in an underlying seam. Only predictions of
the surface subsidence are presented. The material above the coal seam, or so-
called overburden, is represented by three mechanically different ideal
materials: a purely isotropic linear elastic material; an elastoplastic material;
and a horizontally bedded material, which is represented as a series of
horizontal layers of isotropic linear elastic material separated by closely
spaced frictionless interfaces (i.e. bedding planes). The effects of modelling
the caved goaf as a strain-stiffening material, as suggested originally by
Terzaghi (Pappas and Mark, 1993), are also included in the study.
Subsidence profiles observed in a multi-seam coal mine located in New
South Wales, Australia are used to assess the accuracy of the predictions and
to assess which one of the ideal constitutive laws considered here best
represents the overburden material when predicting the displacements of the
coal measure rocks.
2. Longwall panel width
The longwall mining technique is now used widely around the world for the
extraction of coal from underground coal seams. Based on the cover depth
and the panel extraction width, a longwall panel may be classified as being
sub-critical, critical or super-critical in width. For a given height or thickness
of coal extracted, the critical panel width is defined as the width of an
extracted panel for which the maximum possible subsidence is developed
(Mills et al., 2009). The critical width represents the cross-over point from a
“wide” or relatively “shallow” longwall panel to a “narrow” or relatively
“deep” longwall panel. The critical width depends upon the geological
characteristics of the overburden. Extracted panels narrower than the critical
width are deemed to be sub-critical longwall panels. Those wider than the
critical width are known as super-critical longwall panels. The latter are
characterised by a surface subsidence profile that is relatively flat over the
middle portion of the longwall panel. In single seam coal mining operations in
New South Wales, Australia, the critical width of a longwall panel is typically
1–1.6 times the depth of the overburden (McNally et al., 1996; MSEC, 2007a,
b; Mills et al., 2009).
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3. Numerical predictions of subsidence
A realistic numerical simulation of the longwall mining process is likely to
require a three-dimensional (3D) model with progressive coal extraction and
accurate determination of the location and properties of any significant
discontinuities present in the coal measure strata. However, 3D models can be
prohibitively difficult to be constructed, and 3D analyses require substantially
longer computer run times compared to two-dimensional (2D) models.
Furthermore, the accuracy of the predictions obtained from such an explicit
3D model is highly dependent on realistic constitutive laws being used to
represent the mechanics of the coal measure strata.
Subsidence profiles can also be predicted approximately assuming plane-
strain (2D) conditions in the numerical model. Models of this kind have been
considered for both the transverse cross-section (i.e. parallel to the advancing
face) and the longitudinal cross-section (i.e. a slice through the centre of the
longwall). In order to capture the subsidence profile with the largest change in
tilt, transverse cross-sections are considered here.
4. Single seam mining
4.1. Geometry
One of the problems considered in this study is the extraction of a single
longwall panel that is super-critical in geometry. Of interest are predictions of
the maximum surface subsidence Smax, which usually occurs over the middle
region of the single panel, and the subsidence over the edge of the panel, Sedge
(Fig. 1).
Fig. 1. Schematic diagram of a single seam extraction.
The numerical model adopted to examine this problem consists of a cross-
section parallel to the longwall face and assumes plane-strain conditions. The
initial pre-mining geometry of the model has an overburden depth (H) of
150 m, a width of the longwall panel (W) of 300 m, and a height (thickness) of
extraction (T) of 3 m (Figs. 1 and 2a). These dimensions are typical of some
mines in New South Wales, Australia.
Two different options were considered to represent the post mining strata,
designated here as (a) the Cavity Model and (b) the Goaf Model. In the Cavity
Model, it is assumed that a void remains after extraction of the coal seam, as
shown in Fig. 2b, and that subsidence is induced as the void deforms under
geostatic stresses, assuming that the roof and floor of the void can converge
but not overlap. This was implemented using a “self-contact” function in
ABAQUS assuming frictionless contact. Although leaving a void may not be
realistic, this model provides a benchmark for understanding deformation of
the overburden.
(a)
(b)
(c)
Fig. 2. Scale drawing of geometry and material properties of (a) initial conditions, (b) final
conditions for Cavity Model, and (c) final conditions for Goaf Model.
For the Goaf Model, it is assumed that a strain-stiffening material can be
used to represent the behaviour of the caved goaf. This model attempts to
represent the situation where, during and after coal extraction, the material
from the roof of the longwall panel collapses onto the longwall floor and bulks
in volume so as to fill the void left by the extracted coal. The geometry of the
Goaf Model is shown in Fig. 2c. The interface between the caved goaf and the
surrounding strata in the Goaf Model was prescribed assuming frictionless
contact, with no overlapping permitted. The height of the caving above the
longwall floor (hg) in bulking-controlled caving is calculated as follows
(Salamon, 1990):
g1
11
h Tb = + −
(1)
where b is known as the bulking factor. This equation assumes that the
convergence of the longwall roof and floor is much smaller than the extracted
seam height (T). For the cases examined here, it was assumed that the value of
b is 1.2, such that the caved goaf extended to a height of hg = 6T above the
floor of the longwall panel.
4.2. Material behaviour
Three different constitutive laws were used to represent the mechanical
response of the overburden strata: (i) an isotropic linear elastic continuum, (ii)
a conventional linear elastic-perfectly plastic (Mohr-Coulomb) continuum, and
(iii) a horizontally bedded material represented as a series of horizontal layers
of isotropic linear elastic materials separated by closely spaced frictionless
bedding planes simulated by defining frictionless contact interfaces at vertical
intervals of depth D within the material. Details about these constitutive laws
are presented in Suchowerska (2014). In the analyses presented here, the
Young’s modulus of the coal (Ec) was assumed to be equal to that of the
overburden strata (Eo), and both the Young’s modulus and the Poisson’s ratio
(ν) are taken to be constant with depth. Numerical values of the material
properties assumed in the finite element analyses are presented in Table 1.
Table 1. Values of overburden properties used in parametric study. Young’s modulus, Eo (GPa) Poisson’s ratio, ν Cohesion, c (kPa) Friction angle, ϕ (°)
1, 5, 10 0.25 2000 30 Dilation angle, ψ (°)
Unit weight, γ (kN/m3)
Spacing of horizontal bedding planes (m)
30 25 No bedding, 30, 15, 7.5
Although there have been many previous articles that presented predictions
of subsidence assuming an isotropic linear elastic overburden, this case is
included here for completeness. The predictions obtained assuming a linear
H
Sedge Smax
W Longwall
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elastic response of the overburden are useful as a reference when compared to
the results obtained using more sophisticated and complex constitutive laws.
It has been hypothesised by several authors that the caved goaf responds to
loading in a hardening manner (Wardle and Enever, 1983; Smart and Haley,
1987; Trueman, 1990). The caved goaf, which initially is a pile of caved rock,
compacted as the overlying strata deflect and apply load to it. Currently there
are no preferred and generally agreed equations that should be used for the
constitutive law for the caved goaf material. For simplicity, the Terzaghi
(Pappas and Mark, 1993) elastic strain-stiffening material model was used in
this study, where the tangent Young’s modulus (Et) of the goaf material is
specified as
t iE E aσ= + (2)
where Ei is the initial tangent modulus, σ is the applied uniaxial stress acting
on the goaf material, and a is a dimensionless constant. This equation assumes
one-dimensional (1D) compaction conditions in the goaf. The corresponding
stress-strain relationship and the secant modulus (Es) for the caved goaf are
detailed in Morsy and Peng (2002).
The ranges of magnitude suggested for the parameters a and Ei vary
significantly in the literature. For example, values of Ei obtained by Pappas
and Mark (1993) from laboratory testing of caved goaf consisting of shales
and sandstones were 10–15 MPa and 5–6 MPa, respectively. The magnitudes
of the parameters a and Ei, obtained by Morsy and Peng (2002) from back
analysis using a numerical model, were 355 and 31 MPa, respectively. Since it
is not possible to independently assess the most appropriate values for
parameters a and Ei, the complete range of values from previous studies has
been considered, as indicated in Table 2.
Table 2. Parameters used for the Terzaghi strain-stiffening goaf material. Goaf material Ei (MPa) a Reference Stiff 30 350 Morsy and Peng (2002) Average 20 50 - Soft 5 15 Pappas and Mark (1993) Multi-seam 5 38 -
4.3. Subsidence predictions
In all cases considered here, predictions were made of the subsidence
induced by the extraction of a single longwall using the commercial finite
element package ABAQUS. The predicted results for the surface subsidence
are presented here according to the three forms of constitutive laws used to
represent the overburden, with results for the Cavity Model and Goaf Model
presented separately. The analyses were conducted for an initial ratio of
horizontal in situ stress to vertical in situ stress (K) of 1.5.
Tables 3 and 4 provide a summary of the maximum subsidence above the
centre of the longwall (Smax) and the ratio of the subsidence above the edge of
the longwall panel to the maximum subsidence (Sedge/Smax) for all types of
overburden materials used in the Cavity Model and the Goaf Model,
respectively. More detailed information about the results from an extended
form of this study can be found in Suchowerska (2014).
In the sections that follow, subsidence predictions are compared with
typical values for Australian coalfields, ascertained from field measurements.
The measured maximum subsidence above a single seam super-critical
longwall panel (Smax) is typically 55%–65% of the seam’s extracted thickness
(T). The maximum subsidence above the edge of the longwall panel (Sedge) has
been recorded to be within the range of 5%–15% of Smax (Holla, 1985, 1987,
1991; Coulthard and Dutton, 1988). These values should be considered
indicative only, as surface topography and unusual geological features can
lead to anomalies in subsidence profiles (Kay and Carter, 1992; McNally et al.,
1996; Holla and Barclay, 2000). Table 3. Normalised maximum subsidence and edge subsidence - Cavity Model.
Overburden Variable Magnitude Smax/T Sedge/Smax
Elastic Eo 10 GPa 9% 47% 5 GPa 17% 47% 1 GPa 75% 48%
Elastic-perfectly plastic (c = 2000 kPa, ϕ = 30°)
Eo 10 GPa 96% 5% 1 GPa 82% 45%
Bedded material D 30 m 54% 20% 15 m 100% 11% 7.5 m 100% 0.5%
Table 4. Normalised maximum subsidence and edge subsidence - Goaf Model.
Overburden Variable Magnitude Goaf Smax/T Sedge/Smax
Elastic Eo
10 GPa Stiff 4% 50% 1 GPa Stiff 5% 53% 10 GPa Soft 9% 48% 1 GPa Soft 48% 40%
Elastic-perfectly plastic (c = 2000 kPa, ϕ = 30°)
Eo 10 GPa Stiff 4% 50% 10 GPa Ave. 10% 34% 10 GPa Soft 32% 12%
Bedded material D 7.5 m Stiff 6% 28% 7.5 m Ave. 27% 11% 7.5 m Soft 97% 7%
4.3.1. Isotropic linear elastic overburden
Fig. 3 shows the predictions of the normalised subsidence caused by the
extraction of the single super-critical longwall panel, assuming the Cavity
Model, for the case of an isotropic elastic overburden with varying magnitudes
of Young’s modulus (Eo). The maximum subsidence (Smax) for the elastic
overburden when Eo=10 GPa is approximately 9% of the extracted seam
thickness (T). The maximum subsidence (Smax) increases for smaller
magnitudes of Young’s modulus for the overburden (Eo), such that Smax = 75%
of T for Eo=1 GPa. The ratio Sedge/Smax remains constant at approximately 47%
for all magnitudes of Eo considered. Therefore, a softer elastic overburden
increases the maximum predicted subsidence but, as expected for a linear
material, it does not change the overall shape of the subsidence profile. These
results also support previous observations that an isotropic linear elastic
overburden predicts a subsidence profile that is generally shallower and wider
than what is normally observed in the coalfields of New South Wales,
Australia (e.g. Fitzpatrick et al., 1986; Coulthard and Dutton, 1988).
Distance from longwall panel centre
-2W -1W 0W 1W 2W
No
rmal
ised
ver
tical
su
bsid
ence
(S/
T)
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Eo = 10GPa
Eo = 5GPa
Eo = 1GPa
Longwall cavity
Smax
Sedge
Elastic overburden
Fig. 3. Subsidence normalised by extracted seam height for an elastic overburden material
with varying Young’s modulus of the strata (Eo) – Cavity Model.
Fig. 4 shows the subsidence profiles predicted for the Goaf Model with
either a stiff or soft goaf material (Table 2), and with overburden stiffness of
either 1 GPa or 10 GPa. The similar magnitude of the predicted maximum
subsidence of approximately 5% of T for both cases with the stiff goaf
suggests that the subsidence profile is governed more by the stiffness of the
caved goaf material than the overburden stiffness. Indeed, predictions of the
subsurface vertical displacements in the caved goaf and overburden show that
the stiff goaf was compressed to a maximum of approximately 0.1 m.
Correspondingly, the secant modulus of the goaf material rose from its initial
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value of 30 MPa to a maximum of 287 MPa and 239 MPa for an overburden
stiffness of 1 GPa and 10 GPa, respectively.
Distance from longwall panel centre
-2W -1W 0W 1W 2W
Nor
mal
ised
ver
tical
sub
side
nce
(S/
T)
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Stiff goaf, Eo=10GPa
Stiff goaf, Eo=1GPa
Soft goaf, Eo=10GPa
Soft goaf, Eo=1GPa
Caved goaf
Elastic overburden
Fig. 4. Subsidence normalised by extracted seam height for an elastic overburden material
with varying Young’s modulus of the strata (Eo) and goaf material – Goaf Model.
For the cases with the soft goaf, the subsidence profiles shown in Fig. 4 are
quite different for the two magnitudes of Eo. The maximum subsidence is
predicted to be approximately 9% and 48% of T for Eo=10 GPa and Eo=1 GPa,
respectively. Both profiles indicate that generally the subsidence is
significantly larger in magnitude than that predicted for the stiff goaf. A soft
overburden with a relatively soft caved goaf material allows the maximum
subsidence to be achieved, while the sagging limit of a stiff overburden
governs the compression of the caved goaf and the overall surface subsidence.
The secant modulus in the goaf was predicted to rise from an initial value of
5 MPa to the maximum values of 12 MPa and 6 MPa for an overburden
stiffness of 1 GPa and 10 GPa, respectively. The ratio Sedge/Smax for all four
Goaf Model cases is presented in Table 4, and they all fall in the range of
approximately 40%–55%. This result confirms the trend observed in all
predictions with an elastic overburden compared to measurements made in the
field: use of an isotropic elastic overburden overestimates the relative
subsidence above the edge of the longwall panel relative to the maximum
subsidence (Coulthard and Dutton, 1988; Kay et al., 1991).
4.3.2. Elastoplastic overburden
Fig. 5 presents the predicted subsidence for the Cavity Model for two
magnitudes of Eo, when the overburden material is assumed to be an elastic-
perfectly plastic material. Shear failure in the overburden is defined by the
Mohr-Coulomb criterion with cohesion c=2000 kPa and friction angle φ=30°.
These strength parameters were selected based on the findings presented by
Suchowerska (2014), who assumed associated plastic flow (ψ=φ) and
concluded that a friction angle of φ=30° best predicted the pattern of roof
collapse as compared to field observations. The normalised maximum vertical
subsidence is 96% and 82% of T for Eo=10 GPa and Eo=1 GPa, respectively.
The ratio Sedge/Smax is 5% and 45% for Eo=10 GPa and Eo=1 GPa, respectively.
The decrease in the maximum vertical subsidence with a decrease in Young’s
modulus is somewhat counterintuitive but explained by the effect of plastic
deformation. When the Young’s modulus is relatively large, the overburden
deforms primarily by concentrated plastic shearing (i.e. roof collapse) above
the longwall panel, whereas a low Young’s modulus enables the overburden to
sag elastically prior to the onset of failure. The differing behaviour can be
better appreciated when comparing the subsidence for the elastic-perfectly
plastic overburden to the isotropic linear elastic overburden results, which are
also shown in Fig. 5. The softer overburden undergoes much less plastic strain
than the stiffer overburden before the longwall roof touches the longwall floor,
at which point further vertical displacement effectively ceases.
Distance from longwall panel centre
-2W -1W 0W 1W 2W
No
rmal
ised
ver
tical
su
bsi
den
ce (
S/T
)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Eo=10GPa
Eo=1GPa
Longwall cavityElastic-perfectly plastic overburden
Isotropic elasticoverburden, Eo=10GPa
Isotropic elasticoverburden, Eo=1GPa
Fig. 5. Normalised surface subsidence for an elastic-perfectly plastic overburden with
varying Young’s modulus – Cavity Model. Isotropic linear elastic overburden results have
been included for comparison.
Predicted distributions of the vertical displacement for the elastic-perfectly
plastic overburden show that there is effectively a mass downward movement
of a trapezium-shaped block of the overburden directly above the extracted
longwall panel. This failure mechanism has previously been described as
Terzaghi’s trap door problem. The overall shape of the subsidence curves (Fig.
5) appears to be primarily governed by the elastic properties of the overburden
outside the area of failure, and by the plastic flow rule in the thin failure zone
defining the trapezium-shaped block of overburden. For this reason, the
subsidence bowl is still relatively wide for the case where Eo = 1 GPa.
Fig. 6 shows the subsidence profiles for the Goaf Model for the elastic-
perfectly plastic overburden with c=2000 kPa and Eo=10 GPa for three values
of caved goaf stiffness (Table 2). For the stiff goaf case, the maximum
subsidence corresponds to that predicted assuming an isotropic elastic
overburden because the goaf does not permit the overburden to yield. On the
other hand, the overburden above the average goaf and soft goaf yields in both
cases in the manner described above. The maximum vertical subsidence is
10% and 32% of T for the average goaf and soft goaf, respectively. The ratio
Sedge/Smax decreases as the stiffness of the goaf is reduced, such that Sedge/Smax
is 12% for the soft goaf.
Fig. 6. Normalised surface subsidence for an elastic-perfectly plastic overburden with
varying Young’s modulus – Goaf Model.
Additional cases that allow softening of the elastoplastic overburden have
been considered by Suchowerska (2014) but are not discussed in detail here
due to space limitations. Preliminary simulations suggest that strain-softening
of the overburden may reduce the ratio of the subsidence over the edge of the
Distance from longwall panel centre
-2W -1W 0W 1W 2W
Nor
mal
ised
ve
rtic
al s
ubsi
denc
e (
S/T
)
-0.3
-0.2
-0.1
0.0
Stiff goafAverage goafSoft goaf
Caved goaf
c=2000kPa, ϕ =30oc=2000 kPa, ϕ=30°
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longwall panel to the subsidence over the centre (Sedge/Smax). However, robust
implementation of the strain-softening constitutive laws in DFEM is required.
4.3.3. Bedded overburden
Fig. 7 shows that the inclusion of smooth interfaces in an elastic overburden
(Eo =10 GPa) increases the maximum subsidence and also changes the shape
of the subsidence profile in the Cavity Model. Smooth interfaces vertically
spaced at intervals (denoted by the parameter D) of 15 m or less allow the
cavity roof to touch the floor of the longwall panel and the subsidence to reach
100% of T. The relative subsidence at the panel edge (Sedge/Smax) reduces from
47% for the elastic overburden down to 1% for the elastic overburden with
smooth interfaces spaced at 7.5 m intervals (Table 3).
The results presented in Fig. 8 are for the Goaf Model with an elastic
overburden (Eo =10 GPa) and smooth horizontal interfaces spaced every 7.5 m
vertically. Three degrees of stiffness were considered for the strain-stiffening
goaf material, with the relevant parameters provided in Table 2. It is evident
from Fig. 8 that the stiffness of the strain-stiffening goaf material again
governs the maximum subsidence. The soft goaf model predicts that the
maximum subsidence reaches almost the full extracted seam height. The
average goaf and stiff goaf models predict a maximum subsidence of 27% and
6% of T, respectively. The selection of appropriate values for the strain-
stiffening goaf parameters would need to be further investigated, possibly
through back calculation, in order to achieve a prediction of maximum
subsidence equal to the magnitudes typically recorded in the field. This is
conducted in the multi-seam case study presented below.
Distance from longwall panel centre
-2W -1W 0W 1W 2W
No
rmal
ised
ver
tical
su
bsi
den
ce (
S/T
)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
D =30mD =15mD =7.5m
Longwall cavity
Elastic overburdenwith smooth interfaces
Isotropic elasticoverburden
Fig. 7. Normalised surface subsidence for an elastic overburden material containing
smooth horizontal interfaces separated by spacing D – Cavity Model.
Distance from longwall panel centre
-2W -1W 0W 1W 2W
No
rmal
ised
ver
tical
su
bsi
den
ce (
S/T)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Soft goafAve. goafStiff goaf
Caved goaf
Elastic overburdenwith smooth interfaces
Fig. 8. Normalised surface subsidence for an elastic overburden material containing
smooth horizontal interfaces spaced every 7.5 m – Goaf Model.
4.4. Discussion
The results of the simulations of single seam, super-critical longwall mining
presented above indicate that modelling the overburden rock mass as an
isotropic linear elastic medium results in subsidence profiles that extend over a
large region. Such a simple model is known to have numerous shortcomings
when used to predict the profile of surface subsidence above super-critical
longwalls in Australia, and possibly elsewhere. Field measurements indicate
that the actual profile is more likely to be deeper and narrower than the wide,
shallow profile predicted by the linear elastic model.
Although not explored in this paper, it is well known that the predicted
subsidence profile is more like what is observed in the field, if a transversely
isotropic elastic model is adopted for the overburden in place of the isotropic
counterpart. If subsidence prediction for single seam mining is the only
concern, then the selection of transverse isotropy may be adequate for
numerical modelling. However, it is noted that even then, predictions of other
aspects of the rock mass behaviour may be unsatisfactory. For example,
Suchowerska (2014) has shown that selection of the transversely isotropic
elastic overburden may result in inappropriate predictions of the post-mining
stresses around a longwall. Obviously, such predictions will be important
when considering the stability of mine pillars, and they may even become
critical when attempting to predict the subsidence for multi-seam mining.
Namely, when predicting the incremental subsidence due to mining of a
second underlying coal seam, it will be important to have accurate knowledge
of the stresses induced in that underlying seam due to the earlier mining of the
overlying seam. That particular stress state will form the starting point for
modelling the effects of the second seam extraction.
As pointed out by Suchowerska (2014), if the primary goal of a numerical
model is to predict accurately the subsidence due to multi-seam mining, then
the constitutive models used for the overburden would need to ensure
prediction of an appropriate shape for the subsidence profile, as well as allow
for the weight of the overburden to be transferred through the goaf formed
above the first seam onto the material between the coal seams, or so-called
interburden. The results presented thus far indicate that an appropriate
subsidence profile is likely to be predicted assuming a model with a strain-
stiffening goaf material, in conjunction with an overburden composed of
layers of linear elastic material separated by horizontal planes with limited
ability to transmit horizontal shear stress. Furthermore, Suchowerska (2014)
demonstrated quite clearly that such a model also has the potential to predict
accurately the transfer of the overburden load through the goaf to the
underlying strata.
5. Multi-seam mining layouts
It is possible to conceive a variety of feasible layouts of longwall panels for
a multi-seam mining operation. The two particular layouts illustrated
schematically in Fig. 9b and c, referred to as the “stacked” and “staggered”
respectively, are considered here.
For the predictions presented, the initial geometry consists of an overburden
thickness above the first seam (H) of 150 m and an interburden thickness
between the first and second seams (B) of 40 m. For both models the width of
each longwall panel (W) is assumed to be 300 m and the height of extraction
in the first seam (T1) and the second seam (T2) is 3 m. In the stacked
arrangement, the longwall panel extracted in the second seam lies directly
beneath the longwall panel extracted in the first seam (Fig. 9b). In the
staggered arrangement, two longwall panels are extracted in the first seam and
one longwall panel is subsequently extracted in the second seam. The
centreline of the longwall in the second seam aligns with the centre of the
chain pillar in the overlying seam (Fig. 9c).
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Due to space limitations, predictions of subsidence will be presented here
only for the staggered arrangement of multi-seam panels and for a limited set
of material properties. For these predictions, Young’s modulus for all coal
measure strata was kept constant at E = Eo = Ec = 10 GPa. Each goaf was
modelled as a strain-stiffening material with the properties defined for the
multi-seam case identified in Table 2. For consistency with the general
findings of the study of surface subsidence due to single seam mining, both the
overburden and interburden were modelled in this case as a “bedded” material
consisting of horizontal layers of isotropic linear elastic rock separated by
frictionless horizontal interfaces at 5 m vertical spacing.
H Eo
Initial conditions
EoB
E=10GPa
Ec
T1
T2
(a)
WStrain stiffening goaf
Stacked arrangement
Void
(b)
WStrain stiffening goaf
Staggered arrangement
Void
(c)
Fig. 9. Schematic drawing of geometry and material properties of (a) initial conditions of
both stacked and staggered arrangements, (b) final conditions for the stacked arrangement,
and (c) final conditions for the staggered arrangement. As a scale drawing, the void in the
second seam is placed as marked but cannot be seen in the figure.
5.1. Subsidence predictions
Fig. 10a shows the predicted incremental subsidence after the extraction of
the two longwall panels in the first seam of the staggered arrangement. The
maximum subsidence above the centre of each longwall panel in the first seam
is 48% of T1. The superposition of the subsidence above each longwall panel
for the bedded overburden does not cause the ground surface above the chain
pillar to subside and this is because the sagging of the bedded overburden
strata is limited primarily to the width of each individual longwall panel.
The curve plotted in Fig. 10b shows the predicted incremental subsidence
after extraction of the longwall panel in the second seam for the staggered
arrangement. The maximum incremental subsidence above the longwall
panels in the second seam was approximately 100% of T2 for the bedded
overburden and interburden considered here.
5.2. Discussion
The load distribution at the depth of the first seam in the staggered
arrangement can effectively be simplified to a point load being applied to the
mid-span of the interburden beam at the location of the chain pillar dividing
the two longwall panels. This load distribution gives rise to additional
deflection of the interburden and the subsequent increased incremental
subsidence upon extraction of the longwall panel in the second seam.
It has been hypothesised that the additional subsidence typically recorded
above multi-seam longwall panels may be caused by additional compaction of
the caved goaf material above the first seam due to extraction of the second
seam. Such a mechanism has not been observed in the modelling described in
this paper. The results obtained in the sensitivity study conducted by
Suchowerska (2014), and illustrated here, confirm that it would only be
possible to replicate this additional displacement in the first seam goaf in a
continuum approach, such as the finite element method (FEM), if there are
additional stresses applied to the caved goaf material. However, additional
compaction is deemed to be unlikely if the magnitude of the vertical stress in
the centre of the first seam longwall panel has already returned to the
magnitude of the original overburden stress after extracting the first seam. It
is understood that the FEM would not be able to simulate well, if at all, the
displacements that might occur due to rock fragments in the first seam
reconfiguring into a more compact arrangement. Further investigation is
required to see if other numerical methods, such as the discrete element
method (DEM), would be able to represent the reconfiguration of the first
seam caved goaf as a result of extracting a second seam longwall, and if this
would lead to the appropriate shape of the subsidence profile recorded above
multi-seam longwall panels.
(a)
(b)
Fig. 10. Plots of incremental subsidence profiles from the staggered arrangement after
extraction of the longwall in (a) the first seam and (b) the second seam.
6. Multi-seam subsidence case study
In this section, subsidence predictions from numerical simulations are
compared to field observations of the surface subsidence above a multi-seam
mining operation at Blakefield South in the Hunter Valley of New South
Wales, Australia. The Blakefield South under-ground coal mine is part of the
Bulga Complex, which is located approximately 5 km north of the town Broke
in the Upper Hunter Valley. Current mining operations by GlencoreXstrata
Pty Ltd. involve extraction of longwall panels from the Blakefield coal seam,
No
rmal
ised
incr
emen
tal s
ubs
iden
ce (
S/T 2
)
Distance from second seam longwall panel centre
-2W -1W 0W 1W 2W
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Bedded
Caved goaf
Cavity
1st seam
2nd seamBedded interburden
OverburdenCaved goaf
Distance from chain pillar centre in the first seam
-2W -1W 0W 1W 2W
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Bedded
Caved goaf1st seam
2nd seamInterburden
OverburdenCaved goaf
No
rmal
ised
incr
emen
tal s
ubs
iden
ce (
S/T 1
)
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which undermine the previously extracted longwall workings in the Lower
Whybrow coal seam. The Bulga Complex is part of the Hunter coalfields
which together with the Newcastle coalfield, Western coalfields, and Southern
coalfields are part of the Sydney Basin. The Sydney Basin contains sediments
from the early Permian to Triassic. The Lower Whybrow and Blakefield
seams lie within the Jerry Plains Subgroup of the Wittigham Coal Measures
(Stevenson et al., 1998) and mainly comprise bedded sandstones and siltstones.
Within the case study mine site, the surface topography is generally flat to
undulating. Both the Lower Whybrow and Blakefield seams generally dip
from the north down to the south. The depth to the Whybrow seam varies
from 40 m at the northern end of the site to 350 m at the southern end of the
site. The overburden consists of moderate strength strata near the surface
(uniaxial compressive strength (UCS)=30–40 MPa) and at greater depth
consists of interbedded sandstones with an increased strength (UCS=50–
80 MPa). The thickness of the interburden varies between 70 m and 100 m.
The interburden strata comprise interbedded weak to moderate strength units
(UCS=~20–50 MPa). More detailed information about the geology of the site
can be found in the reports by MSEC (2008, 2011) and SCT (2008).
A plan showing the layout of the various longwall panels at the Blakefield
South mine is presented in Fig. 11. The panel of interest here is designated as
BSLW2. It is noted that panels in the Lower Blakefield seam are oblique to
the panels in the overlying Lower Whybrow seam. Fig. 11 also indicates the
DL survey line along which measurements of surface subsidence were made
and used in this case study.
Fig. 11. Map showing the survey lines used to monitor the subsidence when extracting
longwall BSLW2 (MSEC, 2013).
A modified version of the multi-seam numerical model described
previously has been adopted in this case study. Scale drawings of the initial
and final conditions of the multi-seam case-study models used are shown in
Fig. 12a and b, respectively. The dimensions of the models reflect the
geometry of the excavations of BSLW2 and the overlying LW2 and LW3: An
overburden height (H) of 155 m, an interburden thickness (B) of 80 m, a width
of longwall BSLW2 (W) of 410 m, and a coal seam thickness of the Blakefield
seam (T2) of 2.8 m were used. The original width of the panels in the
overlying Lower Whybrow seam was 210 m. However, because the DL
survey line crosses LW2 and LW3 on a diagonal, the width of LW2 and LW3
was assumed to be 242 m in the cross-section used in the numerical model.
The extracted height in the overlying Lower Whybrow seam (T1) was 2.5 m.
The overburden and interburden were modelled as a bedded material, which
consisted of an elastic material with horizontal frictionless interfaces that were
equally spaced at a vertical distance (D) of 5 m. The relevant constitutive
properties are listed in Table 5.
H=155mT1=2.5m
Ec
Eo
E=10GPaInitial conditions
B=80m T2=2.8m Eo
(a)
W=242m
Strain stiffening goaf
Cavity model
Void
W=242m
W=410m
(b)
Fig. 12. Scale drawings of the geometry and material properties used in the numerical
models to predict subsidence above BSLW2 in the Blakefield seam, with (a) initial
conditions and (b) final conditions.
Table 5. Case study parameters.
Young’s modulus, Eo (GPa)
Poisson’s ratio, ν Unit weight, γ (kN/m3)
Spacing of horizontal bedding planes, D (m)
10 0.25 25 5
A strain-stiffening goaf was included in the first seam as well at the second
seam longwall panels. The parameters assumed for the first seam strain-
stiffening goaf were b = 1.2, Ei = 5 MPa and a = 38, as these magnitudes
yielded appropriate subsidence profiles upon extraction of the first seam
longwall panels that matched field measurement (Suchowerska, 2014). For the
second seam, a bulking ratio of b = 1.2 was assumed, such that the caved goaf
height (hg) would correspond to 16.8 m. In order to achieve a subsidence
profile similar in magnitude to the field measurements, the assumed values for
the strain-stiffening parameters of the caved goaf in the second seam were
adjusted to Ei = 4 MPa and a = 40.6 to achieve a better match between the
predicted and measured subsidence profiles. All other specifications of the
multi-seam case-study model were as per the description provided previously.
6.1. Subsidence predictions
Fig. 13 shows the predicted incremental subsidence for the extraction of
BSLW2 using the multi-seam case-study model with a bedded overburden and
interburden. The maximum predicted subsidence is 91% of T2, and the
subsidence above the edges of longwall BSLW2 is predicted to be
approximately 5% of T2. The subsidence predicted above areas of caved
longwall goaf present in both seams is approximately 79% of T2, which
matches the measured subsidence quite well. The predicted subsidence located
above the chain pillar and the edges of the caved goaf present in the first seam
workings does not match the recorded subsidence measurements. The
maximum predicted subsidence occurs above the chain pillar present in the
first seam workings. The finite element model is able to match approximately
the general subsidence profile, but not the local variation close to the chain
pillar.
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Distance from centreline of BSLW2
-1.0W -0.5W 0.0W 0.5W 1.0W
No
rmal
ised
incr
emen
tal v
ertic
al s
ubs
iden
ce (
S/T
2)
-1.1
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
Ei = 5MPa, a = 38
Ei = 3MPa, a = 40.6
BSLW2
Goaf modelBedded overburden, D=5m
Measured: BSLW2
LW2LW3
(a)
Subsidence dueto sagging strata
Subsidence dueto compression
of first seam goaf
(b)
Fig. 13. (a) Normalised incremental subsidence for BSLW2 predicted using the Goaf
Model with a bedded overburden and the normalised measured subsidence for BSLW2
along DL survey line (values of Ei and a identified in the legend correspond to the second
seam); (b) Inferred subsurface deformations contributing to the subsidence recorded at the
ground surface.
6.2. Discussion
One explanation for the inability of the finite element model to capture local
variations in the subsidence profile is the possible existence of several separate
subsurface deformation mechanisms: (i) sagging of the interburden and
overburden, (ii) additional compaction of the caved goaf material at the depth
of the first extracted seam, or (iii) a complex combination of deformation that
is highly dependent on the local geology. It could be postulated that all the
subsidence larger than that recorded above the first seam chain pillar is due to
compaction of the first seam goaf. The relative contribution of the first two
forms of subsurface deformation to the overall subsidence profile is
schematically shown for the case-study DL survey line in Fig. 13b. The
comparison between the predictions and measurements (Fig. 13a) suggests
that the finite element model is not able to replicate displacements associated
with remobilisation and compaction of the first seam goaf. For the predictions
shown in this comparison, the subsidence profile assumed to be generated by
sagging of the interburden and overburden (as shown in Fig. 13b) was
achieved by using the same properties for the second seam goaf as adopted for
the first seam goaf (b=1.2, Ei=5 MPa, and a=38). The predicted subsidence
curve is a reasonable shape for a super-critical longwall panel, except for the
fact that the maximum subsidence occurs directly above the Lower Whybrow
chain pillar. This occurs because the chain pillar in the first seam attracts more
vertical stress than the adjacent strain-stiffening goaf, as a consequence of the
isotropic elastic overburden layers redistributing stress to surrounding strata.
In summary, it is noted that the FEM was able to predict reasonably well the
basic subsidence profile created above the multi-seam longwall panels due to
sagging of the interburden and the overburden. However, it was not successful
in predicting the local variations of subsidence above the chain pillars in the
first seam, which is hypothesised to be generated by compaction of the goaf in
the first seam.
7. Conclusions
A theoretical study to investigate the subsidence profiles predicted above
single and multi-seam longwall panels has been described. Three forms of
constitutive laws were used to represent the coal measure strata in finite
element modelling of the problem. When the overburden and interburden
were represented by a bedded material, consisting of horizontal layers of
isotropic linear elastic material separated by smooth horizontal interfaces, the
predicted subsidence profiles best matched typical field measurements. This
was the case for both single and multi-seam extraction, with the latter
involving a staggered arrangement of longwall panels.
The subsidence measured in a field case above a multi-seam extraction
using the longwall method was compared to predictions of subsidence using
the DFEM. The multi-seam model with a strain-stiffening caved goaf in both
seams and a bedded overburden and interburden was able to match the general
shape of the subsidence profile that formed above the longwall panel extracted
in the second seam. However, the DFEM was not able to predict the variation
in the surface subsidence profile immediately adjacent to the chain pillar in the
first seam, presumably because it was not able to replicate the remobilisation
and compaction of the first seam goaf.
The significance of the research presented here for multi-seam mine
designers is that the general shape of the subsidence profile above a multi-
seam longwall panel can be achieved with finite element modelling. However,
further investigations are required to be able to match more closely the
locations of the maximum and minimum subsidences measured above multi-
seam longwall panels.
Conflict of interest
The authors wish to confirm that there are no known conflicts of interest
associated with this publication and there has been no significant financial
support for this work that could have influenced its outcome.
Acknowledgements
Some of the work described in this paper was supported by the Australian
Research Council in the form of a Discovery Grant and funding through the
Centre of Excellence for Geotechnical Science and Engineering. The authors
also wish to acknowledge the cooperation of Glencore Xstrata Pty Ltd. in
providing data and field measurements for the Blakefield South colliery case
study and the assistance of Mine Subsidence Engineering Consultants.
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Dr. Anastasia M. Suchowerska Iwanec works as a geotechnical engineer for Golder Associates in the Sydney office. Having been awarded a
Bachelor of Civil Engineering from The University of Sydney (2009), she went on to attaining a Ph.D. from The University of Newcastle (2014). Her
research topics have included mechanics of single- and multi-seam longwall coal mining and the mechanical behaviour of lateritic soils from New
Caledonia. Between her studies at university, Anastasia worked for Douglas Partners as a graduate geotechnical engineer where she conducted
fieldwork around NSW, Australia. She is currently involved in undertaking site investigations and design of the NorthConnex and Sydney Metro
tunnels.
Contact information: Golder Associates, 124 Pacific Highway, St Leonards, NSW 2065, Sydney, Australia
Tel: +61 2 9478 3909
E-mail: [email protected]
Dr. John P. Carter is Emeritus Professor and former Dean of Engineering at the University of Newcastle, Australia. He received his bachelor degree
in civil engineering and PhD in geomechanics from the University of Sydney. He has also worked in various teaching and research roles at the
University of Sydney, University of Queensland, Cambridge University and Cornell University. He has broad research interests in soil and rock
mechanics, including computational geomechanics.
Contact information: ARC Centre of Excellence for Geotechnical Science and Engineering, The University of Newcastle, EA, University Drive,
Callaghan, NSW 2308, Australia
Tel: +61 2 4921 5893
E-mail : [email protected]
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Dr. Jim P. Hambleton is an early career academic working in the ARC Centre of Excellence for Geotechnical Science and Engineering at The
University of Newcastle, Australia. He received his PhD in civil engineering (geomechanics) from the University of Minnesota, where he also
completed bachelor’s and master’s degrees in structural engineering and geomechanics, respectively. His main research interests are in computational
mechanics, plasticity, geotechnical analysis, contact mechanics, soil-structure interaction, and soil-machine interaction (SMI).
Contact information: ARC Centre of Excellence for Geotechnical Science and Engineering, The University of Newcastle, EA215, University Drive,
Callaghan, NSW 2308, Australia
Tel: +61 2 4921 5893
E-mail: [email protected]